The annual interest rate and the effective interest rate can be two very different numbers because of the effects of interest compounding. Knowing the effective interest rate is important for small business when determining which bank is offering the best loan or which investment is offering the highest rate of return. The effective interest rate is also known as the annual percentage yield, or APY.
Explain that banks and other lenders may compound interest more than once per year. For example, when you take out a loan that requires monthly payments, the interest on the account is compounded each month rather than once per year.
Show how to calculate the periodic interest rate from the annual rate by dividing the annual rate by the number of times per year interest is compounded. For example, if you had a loan with a 12 percent annual rate that compounds interest monthly, you would divide 12 by 12 to find the period rate, in this case the monthly rate, equals 1 percent.
Demonstrate that interest compounded more than once per year will accrue additional interest over the remainder of the year. For example, if you have a $5,000 loan at 12 percent annually that compounds interest monthly, the first month $50 of interest would accrue, making the balance of the account $5,050. The next month, $50.50, not $50, would accrue, making the balance $5,100.50.
Define the effective interest rate as the amount of interest that will accrue on the account over the course of one year when interest compounding is taken into account.
Present the formula for calculating the effective interest rate as the quantity 1 plus the periodic rate raised to the power of the number of times per year interest is compounded minus 1, or (1+P)^C-1, where P is the periodic rate and C is the number of times per year interest is compounded.
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